TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - Fare Planning for Public Transport N2 - In this paper we introduce the fare planning problem for public transport which consists in designing a system of fares maximizing revenue. We propose a new simple general model for this problem. It i s based on a demand function and constraints for the different fares. The constraints define the structure of the fare system, e.g., distance dependent fares or zone fares. We discuss a simple example with a quadratic demand function and distance dependent fares. Then we introduce a more realistic discrete choice model in which passengers choose between different alternatives depending on the numb er of trips per month. We demonstrate the examples by computational experiments. T3 - ZIB-Report - 05-20 KW - fare planning KW - demand function KW - discrete choice model Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8541 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - The Steiner Connectivity Problem N2 - The Steiner connectivity problem is a generalization of the Steiner tree problem. It consists in finding a minimum cost set of simple paths to connect a subset of nodes in an undirected graph. We show that polyhedral and algorithmic results on the Steiner tree problem carry over to the Steiner connectivity problem, namely, the Steiner cut and the Steiner partition inequalities, as well as the associated polynomial time separation algorithms, can be generalized. Similar to the Steiner tree case, a directed formulation, which is stronger than the natural undirected one, plays a central role. T3 - ZIB-Report - 09-07 KW - Steiner Tree KW - Partition Inequalities KW - Paths KW - Connectivity KW - Generalization Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11171 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Pfetsch, Marc T1 - Nonlinear pseudo-Boolean optimization: relaxation or propagation? N2 - Pseudo-Boolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudo-Boolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a linear programming relaxation or one can treat them directly by propagation. In this paper, we investigate the individual strengths of these approaches and compare their computational performance. Furthermore, we integrate these techniques into a branch-and-cut-and-propagate framework, resulting in an efficient nonlinear pseudo-Boolean solver. T3 - ZIB-Report - 09-11 KW - Pseudo-Boolean KW - constraint integer programming KW - linear relaxation KW - separation algorithm KW - domain propagation Y1 - 2009 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11232 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - The Line Connectivity Problem N2 - This paper introduces the "line connectivity problem", a generalization of the Steiner tree problem and a special case of the line planning problem. We study its complexity and give an IP formulation in terms of an exponential number of constraints associated with "line cut constraints". These inequalities can be separated in polynomial time. We also generalize the Steiner partition inequalities. T3 - ZIB-Report - 08-31 KW - Steiner Tree Generalization Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10820 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Pfetsch, Marc T1 - Detecting Orbitopal Symmetries N2 - Orbitopes can be used to handle symmetries which arise in integer programming formulations with an inherent assignment structure. We investigate the detection of symmetries appearing in this approach. We show that detecting so-called orbitopal symmetries is graph-isomorphism hard in general, but can be performed in linear time if the assignment structure is known. T3 - ZIB-Report - 08-33 KW - Symmetrie-Erkennung KW - Orbitope KW - Ganzzahlige Programmierung KW - Symmetrie-Brechung KW - Graphenisomorphie KW - symmetry detection KW - orbitopes KW - integer programming KW - symmetry breaking KW - graph ismorphism Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10842 SN - 1438-0064 ER - TY - GEN A1 - Torres, Luis Miguel A1 - Torres, Ramiro A1 - Borndörfer, Ralf A1 - Pfetsch, Marc T1 - Line Planning on Paths and Tree Networks with Applications to the Quito Trolebus System N2 - Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito Trolebus system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the Trolebus System in Quito can be solved quite well, and significant optimization potentials can be demonstrated. T3 - ZIB-Report - 08-35 KW - line planning KW - computational complexity KW - public transport KW - integer programming Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10869 SN - 1438-0064 ER - TY - GEN A1 - Torres, Luis Miguel A1 - Torres, Ramiro A1 - Borndörfer, Ralf A1 - Pfetsch, Marc T1 - On the Line Planning Problem in Tree Networks N2 - We introduce an optimization model for the line planning problem in a public transportation system that aims at minimizing operational costs while ensuring a given level of quality of service in terms of available transport capacity. We discuss the computational complexity of the model for tree network topologies and line structures that arise in a real-world application at the Trolebus Integrated System in Quito. Computational results for this system are reported. T3 - ZIB-Report - 08-52 KW - line planning KW - computational complexity KW - public transport optimization Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11069 SN - 1438-0064 ER - TY - GEN A1 - Torres, Luis Miguel A1 - Torres, Ramiro A1 - Borndörfer, Ralf A1 - Pfetsch, Marc T1 - Line Planning on Paths and Tree Networks with Applications to the Quito Trolebus System (Extended Abstract) N2 - Line planning is an important step in the strategic planning process of a public transportation system. In this paper, we discuss an optimization model for this problem in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the problem for path and tree network topologies as well as several categories of line operation that are important for the Quito Trolebus system. It turns out that, from a computational complexity worst case point of view, the problem is hard in all but the most simple variants. In practice, however, instances based on real data from the Trolebus System in Quito can be solved quite well, and significant optimization potentials can be demonstrated. T3 - ZIB-Report - 08-53 KW - line planning KW - computational complexity KW - public transport KW - integer programming Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-11076 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Pfetsch, Marc T1 - Solving Pseudo-Boolean Problems with SCIP N2 - Pseudo-Boolean problems generalize SAT problems by allowing linear constraints and a linear objective function. Different solvers, mainly having their roots in the SAT domain, have been proposed and compared,for instance, in Pseudo-Boolean evaluations. One can also formulate Pseudo-Boolean models as integer programming models. That is,Pseudo-Boolean problems lie on the border between the SAT domain and the integer programming field. In this paper, we approach Pseudo-Boolean problems from the integer programming side. We introduce the framework SCIP that implements constraint integer programming techniques. It integrates methods from constraint programming, integer programming, and SAT-solving: the solution of linear programming relaxations, propagation of linear as well as nonlinear constraints, and conflict analysis. We argue that this approach is suitable for Pseudo-Boolean instances containing general linear constraints, while it is less efficient for pure SAT problems. We present extensive computational experiments on the test set used for the Pseudo-Boolean evaluation 2007. We show that our approach is very efficient for optimization instances and competitive for feasibility problems. For the nonlinear parts, we also investigate the influence of linear programming relaxations and propagation methods on the performance. It turns out that both techniques are helpful for obtaining an efficient solution method. T3 - ZIB-Report - 08-12 KW - Pseudo-Boolean KW - Constraint Programming KW - Ganzzahlige Programmierung KW - Branch-And-Cut KW - Optimierungssoftware KW - Pseudo-Boolean KW - constraint integer programming KW - integer programming KW - branch-and-cut KW - optimization software Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10671 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - Models for Fare Planning in Public Transport N2 - The optimization of fare systems in public transit allows to pursue objectives such as the maximization of demand, revenue, profit, or social welfare. We propose a non-linear optimization approach to fare planning that is based on a detailed discrete choice model of user behavior. The approach allows to analyze different fare structures, optimization objectives, and operational scenarios involving, e.g., subsidies. We use the resulting models to compute optimized fare systems for the city of Potsdam, Germany. T3 - ZIB-Report - 08-16 KW - Preisplanung KW - Nachfragefunktion KW - Optimierung KW - Nahverkehr Y1 - 2008 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-10708 SN - 1438-0064 ER - TY - GEN A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - Optimal Fares for Public Transport N2 - The \emph{fare planning problem} for public transport is to design a system of fares that maximize the revenue. We introduce a nonlinear optimization model to approach this problem. It is based on a d iscrete choice logit model that expresses demand as a function of the fares. We illustrate our approach by computing and comparing two different fare systems for the intercity network of the Netherlands. T3 - ZIB-Report - 05-35 KW - fare planning KW - demand function KW - discrete choice model Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-8698 ER - TY - GEN A1 - Harks, Tobias A1 - Heinz, Stefan A1 - Pfetsch, Marc A1 - Vredeveld, Tjark T1 - Online Multicommodity Routing with Time Windows N2 - We consider a multicommodity routing problem, where demands are released \emph{online} and have to be routed in a network during specified time windows. The objective is to minimize a time and load dependent convex cost function of the aggregate arc flow. First, we study the fractional routing variant. We present two online algorithms, called Seq and Seq$^2$. Our first main result states that, for cost functions defined by polynomial price functions with nonnegative coefficients and maximum degree~$d$, the competitive ratio of Seq and Seq$^2$ is at most $(d+1)^{d+1}$, which is tight. We also present lower bounds of $(0.265\,(d+1))^{d+1}$ for any online algorithm. In the case of a network with two nodes and parallel arcs, we prove a lower bound of $(2-\frac{1}{2} \sqrt{3})$ on the competitive ratio for Seq and Seq$^2$, even for affine linear price functions. Furthermore, we study resource augmentation, where the online algorithm has to route less demand than the offline adversary. Second, we consider unsplittable routings. For this setting, we present two online algorithms, called U-Seq and U-Seq$^2$. We prove that for polynomial price functions with nonnegative coefficients and maximum degree~$d$, the competitive ratio of U-Seq and U-Seq$^2$ is bounded by $O{1.77^d\,d^{d+1}}$. We present lower bounds of $(0.5307\,(d+1))^{d+1}$ for any online algorithm and $(d+1)^{d+1}$ for our algorithms. Third, we consider a special case of our framework: online load balancing in the $\ell_p$-norm. For the fractional and unsplittable variant of this problem, we show that our online algorithms are $p$ and $O{p}$ competitive, respectively. Such results where previously known only for scheduling jobs on restricted (un)related parallel machines. T3 - ZIB-Report - 07-22 KW - Online Optimization KW - Routing KW - Telecommunications Y1 - 2007 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-9654 SN - 1438-0064 ER - TY - GEN A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Pfetsch, Marc A1 - Vigerske, Stefan T1 - Large Neighborhood Search beyond MIP N2 - Large neighborhood search (LNS) heuristics are an important component of modern branch-and-cut algorithms for solving mixed-integer linear programs (MIPs). Most of these LNS heuristics use the LP relaxation as the basis for their search, which is a reasonable choice in case of MIPs. However, for more general problem classes, the LP relaxation alone may not contain enough information about the original problem to find feasible solutions with these heuristics, e.g., if the problem is nonlinear or not all constraints are present in the current relaxation. In this paper, we discuss a generic way to extend LNS heuristics that have been developed for MIP to constraint integer programming (CIP), which is a generalization of MIP in the direction of constraint programming (CP). We present computational results of LNS heuristics for three problem classes: mixed-integer quadratically constrained programs, nonlinear pseudo-Boolean optimization instances, and resource-constrained project scheduling problems. Therefore, we have implemented extended versions of the following LNS heuristics in the constraint integer programming framework SCIP: Local Branching, RINS, RENS, Crossover, and DINS. Our results indicate that a generic generalization of LNS heuristics to CIP considerably improves the success rate of these heuristics. T3 - ZIB-Report - 11-21 KW - Large Neighborhood Search KW - Primal Heuristic KW - MIP KW - MIQCP KW - Pseudo-Boolean Y1 - 2011 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-12989 ER - TY - GEN A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Pfetsch, Marc ED - Jünger, Michael ED - Reinelt, Gerhard T1 - Progress in Academic Computational Integer Programming T2 - Facets of Combinatorial Optimization Y1 - 2013 U6 - https://doi.org/10.1007/978-3-642-38189-8_19 SP - 483 EP - 506 PB - Springer ER - TY - BOOK A1 - Koch, Thorsten A1 - Hiller, Benjamin A1 - Pfetsch, Marc A1 - Schewe, Lars T1 - Evaluating Gas Network Capacities Y1 - 2015 SN - 978-1-611973-68-6 PB - SIAM ER - TY - JOUR A1 - Pfetsch, Marc A1 - Fügenschuh, Armin A1 - Geißler, Björn A1 - Geißler, Nina A1 - Gollmer, Ralf A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Martin, Alexander A1 - Morsi, Antonio A1 - Rövekamp, Jessica A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schultz, Rüdiger A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Stangl, Claudia A1 - Steinbach, Marc A1 - Vigerske, Stefan A1 - Willert, Bernhard T1 - Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions JF - Optimization Methods and Software N2 - In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. We describe a two-stage approach to solve the resulting complex and numerically difficult feasibility problem. The first phase consists of four distinct algorithms applying linear, and methods for complementarity constraints to compute possible settings for the discrete decisions. The second phase employs a precise continuous programming model of the gas network. Using this setup, we are able to compute high quality solutions to real-world industrial instances that are significantly larger than networks that have appeared in the mathematical programming literature before. Y1 - 2014 U6 - https://doi.org/10.1080/10556788.2014.888426 PB - Taylor & Francis ER - TY - JOUR A1 - Humpola, Jesco A1 - Joormann, Imke A1 - Oucherif, Djamal A1 - Pfetsch, Marc A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schwarz, Robert T1 - GasLib - A Library of Gas Network Instances JF - Optimization Online N2 - The development of mathematical simulation and optimization models and algorithms for solving gas transport problems is an active field of research. In order to test and compare these models and algorithms, gas network instances together with demand data are needed. The goal of GasLib is to provide a set of publicly available gas network instances that can be used by researchers in the field of gas transport. The advantages are that researchers save time by using these instances and that different models and algorithms can be compared on the same specified test sets. The library instances are encoded in an XML format. In this paper, we explain this format and present the instances that are available in the library. Y1 - 2015 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57950 ER - TY - CHAP A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Pfetsch, Marc A1 - Vigerske, Stefan T1 - Large Neighborhood Search beyond MIP T2 - Proceedings of the 9th Metaheuristics International Conference (MIC 2011) N2 - Large neighborhood search (LNS) heuristics are an important component of modern branch-and-cut algorithms for solving mixed-integer linear programs (MIPs). Most of these LNS heuristics use the LP relaxation as the basis for their search, which is a reasonable choice in case of MIPs. However, for more general problem classes, the LP relaxation alone may not contain enough information about the original problem to find feasible solutions with these heuristics, e.g., if the problem is nonlinear or not all constraints are present in the current relaxation. In this paper, we discuss a generic way to extend LNS heuristics that have been developed for MIP to constraint integer programming (CIP), which is a generalization of MIP in the direction of constraint programming (CP). We present computational results of LNS heuristics for three problem classes: mixed-integer quadratically constrained programs, nonlinear pseudo-Boolean optimization instances, and resource-constrained project scheduling problems. Therefore, we have implemented extended versions of the following LNS heuristics in the constraint integer programming framework SCIP: Local Branching, RINS, RENS, Crossover, and DINS. Our results indicate that a generic generalization of LNS heuristics to CIP considerably improves the success rate of these heuristics. Y1 - 2011 SN - 978-88-900984-3-7 SP - 51 EP - 60 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Karbstein, Marika A1 - Pfetsch, Marc T1 - The Steiner connectivity problem JF - Mathematical Programming A Y1 - 2013 U6 - https://doi.org/10.1007/s10107-012-0564-5 VL - 142 IS - 1 SP - 133 EP - 167 ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Karbstein, Marika A1 - Pfetsch, Marc T1 - Models for Fare Planning in Public Transport JF - Discrete Applied Mathematics Y1 - 2012 U6 - https://doi.org/10.1016/j.dam.2012.02.027 VL - 160 IS - 18 SP - 2591 EP - 2605 ER - TY - JOUR A1 - Schmidt, Martin A1 - Assmann, Denis A1 - Burlacu, Robert A1 - Humpola, Jesco A1 - Joormann, Imke A1 - Kanelakis, Nikolaos A1 - Koch, Thorsten A1 - Oucherif, Djamal A1 - Pfetsch, Marc A1 - Schewe, Lars A1 - Schwarz, Robert A1 - Sirvent, Matthias T1 - GasLib – A Library of Gas Network Instances JF - Data Y1 - 2017 U6 - https://doi.org/10.3390/data2040040 VL - 2 IS - 4 ER - TY - CHAP A1 - Martin, Alexander A1 - Geißler, Björn A1 - Heyn, Christine A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Morsi, Antonio A1 - Pfetsch, Marc A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schultz, Rüdiger A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Steinbach, Marc A1 - Willert, Bernhard T1 - Optimierung Technischer Kapazitäten in Gasnetzen T2 - Optimierung in der Energiewirtschaft Y1 - 2011 SP - 105 EP - 114 PB - VDI-Verlag, Düsseldorf ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc ED - Haasis, Hans-Dietrich ED - Kopfer, Herbert ED - Schönberger, Jörn T1 - Optimal Fares for Public Transport T2 - Operations Research Proceedings 2005 Y1 - 2006 UR - {http://opus.kobv.de/zib/volltexte/2005/869/} SP - 29 EP - 36 PB - Springer-Verlag ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc ED - Barnhart, Cynthia ED - Clausen, Uwe ED - Lauther, Ulrich ED - Möhring, Rolf T1 - Line Planning and Connectivity T2 - Models and Algorithms for Optimization in Logistics Y1 - 2009 IS - 09261 PB - Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany CY - Dagstuhl, Germany ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc T1 - Angebotsplanung im öffentlichen Nahverkehr T2 - HEUREKA’08 Y1 - 2008 UR - http://opus.kobv.de/zib/volltexte/2008/1084/ PB - FGSV Verlag ER - TY - CHAP A1 - Torres, Luis Miguel A1 - Torres, Ramiro A1 - Borndörfer, Ralf A1 - Pfetsch, Marc ED - Fischetti, Matteo ED - Widmayer, Peter T1 - Line Planning on Paths and Tree Networks with Applications to the Quito Trolebus System T2 - ATMOS 2008 - 8th Workshop on Algorithmic Approaches for Transportation Modeling, Optimization, and Systems Y1 - 2008 UR - http://drops.dagstuhl.de/opus/volltexte/2008/1580 PB - Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany CY - Dagstuhl, Germany ER - TY - CHAP A1 - Borndörfer, Ralf A1 - Neumann, Marika A1 - Pfetsch, Marc ED - Fleischmann, Bernhard ED - Borgwardt, Karl ED - Klein, Robert ED - Tuma, Axel T1 - The Line Connectivity Problem T2 - Operations Research Proceedings 2008 Y1 - 2009 UR - http://opus.kobv.de/zib/volltexte/2008/1117/ SP - 557 EP - 562 PB - Springer-Verlag ER - TY - JOUR A1 - Borndörfer, Ralf A1 - Grötschel, Martin A1 - Pfetsch, Marc T1 - Public transport to the fORe JF - OR/MS Today Y1 - 2006 UR - http://www.lionhrtpub.com/orms/orms-4-06/frtransport.html SP - 30 EP - 40 ER - TY - CHAP A1 - Pfetsch, Marc A1 - Borndörfer, Ralf ED - Haasis, Hans-Dietrich T1 - Routing in Line Planning for Public Transportation T2 - Operations Research Proceedings 2005 Y1 - 2006 UR - http://opus.kobv.de/zib/volltexte/2005/870/ SP - 405 EP - 410 PB - Springer-Verlag ER - TY - CHAP A1 - Berthold, Timo A1 - Heinz, Stefan A1 - Pfetsch, Marc ED - Kullmann, Oliver T1 - Nonlinear pseudo-Boolean optimization T2 - Theory and Applications of Satisfiability Testing – SAT 2009 Y1 - 2009 VL - 5584 SP - 441 EP - 446 PB - Springer ER - TY - CHAP A1 - Berthold, Timo A1 - Pfetsch, Marc ED - Fleischmann, Bernhard ED - Borgwardt, Karl ED - Klein, Robert ED - Tuma, Axel T1 - Detecting Orbitopal Symmetries T2 - Operations Research Proceedings 2008 Y1 - 2009 SP - 433 EP - 438 PB - Springer-Verlag ER - TY - CHAP A1 - Koch, Thorsten A1 - Pfetsch, Marc A1 - Rövekamp, Jessica T1 - Introduction T2 - Evaluating Gas Network Capacities Y1 - 2015 SN - 9781611973686 SP - 3 EP - 16 PB - Society for Industrial and Applied Mathematics ER - TY - CHAP A1 - Bargmann, Dagmar A1 - Ebbers, Mirko A1 - Heinecke, Nina A1 - Koch, Thorsten A1 - Kühl, Veronika A1 - Pelzer, Antje A1 - Pfetsch, Marc A1 - Rövekamp, Jessica A1 - Spreckelsen, Klaus T1 - State-of-the-art in evaluating gas network capacities T2 - Evaluating Gas Network Capacities Y1 - 2015 SN - 9781611973686 SP - 65 EP - 84 PB - Society for Industrial and Applied Mathematics ER - TY - CHAP A1 - Schewe, Lars A1 - Koch, Thorsten A1 - Martin, Alexander A1 - Pfetsch, Marc T1 - Mathematical optimization for evaluating gas network capacities T2 - Evaluating Gas Network Capacities Y1 - 2015 SN - 9781611973686 SP - 87 EP - 102 PB - Society for Industrial and Applied Mathematics ER - TY - CHAP A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Lehmann, Thomas A1 - Lenz, Ralf A1 - Morsi, Antonio A1 - Pfetsch, Marc A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Stangl, Claudia A1 - Willert, Bernhard T1 - Computational results for validation of nominations T2 - Evaluating Gas Network Capacities N2 - The different approaches to solve the validation of nomination problem presented in the previous chapters are evaluated computationally in this chapter. Each approach is analyzed individually, as well as the complete solvers for these problems. We demonstrate that the presented approaches can successfully solve large-scale real-world instances. Y1 - 2015 SN - 9781611973686 VL - SIAM-MOS series on Optimization ER - TY - GEN A1 - Hendel, Gregor A1 - Anderson, Daniel A1 - Le Bodic, Pierre A1 - Pfetsch, Marc T1 - Estimating the Size of Branch-And-Bound Trees N2 - This paper investigates the estimation of the size of Branch-and-Bound (B&B) trees for solving mixed-integer programs. We first prove that the size of the B&B tree cannot be approximated within a factor of~2 for general binary programs, unless P equals NP. Second, we review measures of the progress of the B&B search, such as the gap, and propose a new measure, which we call leaf frequency. We study two simple ways to transform these progress measures into B&B tree size estimates, either as a direct projection, or via double-exponential smoothing, a standard time-series forecasting technique. We then combine different progress measures and their trends into nontrivial estimates using Machine Learning techniques, which yields more precise estimates than any individual measure. The best method we have identified uses all individual measures as features of a random forest model. In a large computational study, we train and validate all methods on the publicly available MIPLIB and Coral general purpose benchmark sets. On average, the best method estimates B&B tree sizes within a factor of 3 on the set of unseen test instances even during the early stage of the search, and improves in accuracy as the search progresses. It also achieves a factor 2 over the entire search on each out of six additional sets of homogeneous instances we have tested. All techniques are available in version 7 of the branch-and-cut framework SCIP. T3 - ZIB-Report - 20-02 KW - mixed integer programming KW - machine learning KW - branch and bound KW - forecasting Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78144 SN - 1438-0064 ER - TY - GEN A1 - Pfetsch, Marc A1 - Fügenschuh, Armin A1 - Geißler, Björn A1 - Geißler, Nina A1 - Gollmer, Ralf A1 - Hiller, Benjamin A1 - Humpola, Jesco A1 - Koch, Thorsten A1 - Lehmann, Thomas A1 - Martin, Alexander A1 - Morsi, Antonio A1 - Rövekamp, Jessica A1 - Schewe, Lars A1 - Schmidt, Martin A1 - Schultz, Rüdiger A1 - Schwarz, Robert A1 - Schweiger, Jonas A1 - Stangl, Claudia A1 - Steinbach, Marc A1 - Vigerske, Stefan A1 - Willert, Bernhard T1 - Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions N2 - In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements such that there exists a network state meeting all physical, technical, and legal constraints. We describe a two-stage approach to solve the resulting complex and numerically difficult mixed-integer non-convex nonlinear feasibility problem. The first phase consists of four distinct algorithms facilitating mixed-integer linear, mixed-integer nonlinear, reduced nonlinear, and complementarity constrained methods to compute possible settings for the discrete decisions. The second phase employs a precise continuous nonlinear programming model of the gas network. Using this setup, we are able to compute high quality solutions to real-world industrial instances whose size is significantly larger than networks that have appeared in the literature previously. T3 - ZIB-Report - 12-41 Y1 - 2012 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-16531 SN - 1438-0064 ER - TY - GEN A1 - Maher, Stephen J. A1 - Fischer, Tobias A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gleixner, Ambros A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schenker, Sebastian A1 - Schwarz, Robert A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Weninger, Dieter A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 4.0 N2 - The SCIP Optimization Suite is a powerful collection of optimization software that consists of the branch-cut-and-price framework and mixed-integer programming solver SCIP, the linear programming solver SoPlex, the modeling language Zimpl, the parallelization framework UG, and the generic branch-cut-and-price solver GCG. Additionally, it features the extensions SCIP-Jack for solving Steiner tree problems, PolySCIP for solving multi-objective problems, and SCIP-SDP for solving mixed-integer semidefinite programs. The SCIP Optimization Suite has been continuously developed and has now reached version 4.0. The goal of this report is to present the recent changes to the collection. We not only describe the theoretical basis, but focus on implementation aspects and their computational consequences. T3 - ZIB-Report - 17-12 Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-62170 SN - 1438-0064 ER - TY - GEN A1 - Gamrath, Gerald A1 - Fischer, Tobias A1 - Gally, Tristan A1 - Gleixner, Ambros A1 - Hendel, Gregor A1 - Koch, Thorsten A1 - Maher, Stephen J. A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schenker, Sebastian A1 - Schwarz, Robert A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Vigerske, Stefan A1 - Weninger, Dieter A1 - Winkler, Michael A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 3.2 N2 - The SCIP Optimization Suite is a software toolbox for generating and solving various classes of mathematical optimization problems. Its major components are the modeling language ZIMPL, the linear programming solver SoPlex, the constraint integer programming framework and mixed-integer linear and nonlinear programming solver SCIP, the UG framework for parallelization of branch-and-bound-based solvers, and the generic branch-cut-and-price solver GCG. It has been used in many applications from both academia and industry and is one of the leading non-commercial solvers. This paper highlights the new features of version 3.2 of the SCIP Optimization Suite. Version 3.2 was released in July 2015. This release comes with new presolving steps, primal heuristics, and branching rules within SCIP. In addition, version 3.2 includes a reoptimization feature and improved handling of quadratic constraints and special ordered sets. SoPlex can now solve LPs exactly over the rational number and performance improvements have been achieved by exploiting sparsity in more situations. UG has been tested successfully on 80,000 cores. A major new feature of UG is the functionality to parallelize a customized SCIP solver. GCG has been enhanced with a new separator, new primal heuristics, and improved column management. Finally, new and improved extensions of SCIP are presented, namely solvers for multi-criteria optimization, Steiner tree problems, and mixed-integer semidefinite programs. T3 - ZIB-Report - 15-60 KW - mixed-integer linear and nonlinear programming KW - MIP solver KW - MINLP solver KW - linear programming KW - LP solver KW - simplex method KW - modeling KW - parallel branch-and-bound KW - branch-cut-and-price framework KW - generic column generation KW - Steiner tree solver KW - multi-criteria optimization KW - mixed-integer semidefinite programming Y1 - 2016 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-57675 SN - 1438-0064 ER - TY - GEN A1 - Gamrath, Gerald A1 - Anderson, Daniel A1 - Bestuzheva, Ksenia A1 - Chen, Wei-Kun A1 - Eifler, Leon A1 - Gasse, Maxime A1 - Gemander, Patrick A1 - Gleixner, Ambros A1 - Gottwald, Leona A1 - Halbig, Katrin A1 - Hendel, Gregor A1 - Hojny, Christopher A1 - Koch, Thorsten A1 - Le Bodic, Pierre A1 - Maher, Stephen J. A1 - Matter, Frederic A1 - Miltenberger, Matthias A1 - Mühmer, Erik A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Tawfik, Christine A1 - Vigerske, Stefan A1 - Wegscheider, Fabian A1 - Weninger, Dieter A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 7.0 N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming frame- work SCIP. This paper discusses enhancements and extensions contained in version 7.0 of the SCIP Optimization Suite. The new version features the parallel presolving library PaPILO as a new addition to the suite. PaPILO 1.0 simplifies mixed-integer linear op- timization problems and can be used stand-alone or integrated into SCIP via a presolver plugin. SCIP 7.0 provides additional support for decomposition algorithms. Besides im- provements in the Benders’ decomposition solver of SCIP, user-defined decomposition structures can be read, which are used by the automated Benders’ decomposition solver and two primal heuristics. Additionally, SCIP 7.0 comes with a tree size estimation that is used to predict the completion of the overall solving process and potentially trigger restarts. Moreover, substantial performance improvements of the MIP core were achieved by new developments in presolving, primal heuristics, branching rules, conflict analysis, and symmetry handling. Last, not least, the report presents updates to other components and extensions of the SCIP Optimization Suite, in particular, the LP solver SoPlex and the mixed-integer semidefinite programming solver SCIP-SDP. T3 - ZIB-Report - 20-10 Y1 - 2020 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-78023 SN - 1438-0064 ER - TY - GEN A1 - Gleixner, Ambros A1 - Eifler, Leon A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gemander, Patrick A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Hojny, Christopher A1 - Koch, Thorsten A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schlösser, Franziska A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Viernickel, Jan Merlin A1 - Vigerske, Stefan A1 - Weninger, Dieter A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 5.0 N2 - This article describes new features and enhanced algorithms made available in version 5.0 of the SCIP Optimization Suite. In its central component, the constraint integer programming solver SCIP, remarkable performance improvements have been achieved for solving mixed-integer linear and nonlinear programs. On MIPs, SCIP 5.0 is about 41 % faster than SCIP 4.0 and over twice as fast on instances that take at least 100 seconds to solve. For MINLP, SCIP 5.0 is about 17 % faster overall and 23 % faster on instances that take at least 100 seconds to solve. This boost is due to algorithmic advances in several parts of the solver such as cutting plane generation and management, a new adaptive coordination of large neighborhood search heuristics, symmetry handling, and strengthened McCormick relaxations for bilinear terms in MINLPs. Besides discussing the theoretical background and the implementational aspects of these developments, the report describes recent additions for the other software packages connected to SCIP, in particular for the LP solver SoPlex, the Steiner tree solver SCIP-Jack, the MISDP solver SCIP-SDP, and the parallelization framework UG. T3 - ZIB-Report - 17-61 KW - constraint integer programming KW - linear programming KW - mixed-integer linear programming KW - mixed-integer nonlinear programming KW - optimization solver KW - branch-and-cut KW - branch-and-price KW - column generation framework KW - parallelization KW - mixed-integer semidefinite programming KW - Steiner tree optimization Y1 - 2017 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-66297 SN - 1438-0064 ER - TY - GEN A1 - Gleixner, Ambros A1 - Bastubbe, Michael A1 - Eifler, Leon A1 - Gally, Tristan A1 - Gamrath, Gerald A1 - Gottwald, Robert Lion A1 - Hendel, Gregor A1 - Hojny, Christopher A1 - Koch, Thorsten A1 - Lübbecke, Marco A1 - Maher, Stephen J. A1 - Miltenberger, Matthias A1 - Müller, Benjamin A1 - Pfetsch, Marc A1 - Puchert, Christian A1 - Rehfeldt, Daniel A1 - Schlösser, Franziska A1 - Schubert, Christoph A1 - Serrano, Felipe A1 - Shinano, Yuji A1 - Viernickel, Jan Merlin A1 - Walter, Matthias A1 - Wegscheider, Fabian A1 - Witt, Jonas T. A1 - Witzig, Jakob T1 - The SCIP Optimization Suite 6.0 N2 - The SCIP Optimization Suite provides a collection of software packages for mathematical optimization centered around the constraint integer programming framework SCIP. This paper discusses enhancements and extensions contained in version 6.0 of the SCIP Optimization Suite. Besides performance improvements of the MIP and MINLP core achieved by new primal heuristics and a new selection criterion for cutting planes, one focus of this release are decomposition algorithms. Both SCIP and the automatic decomposition solver GCG now include advanced functionality for performing Benders’ decomposition in a generic framework. GCG’s detection loop for structured matrices and the coordination of pricing routines for Dantzig-Wolfe decomposition has been significantly revised for greater flexibility. Two SCIP extensions have been added to solve the recursive circle packing problem by a problem-specific column generation scheme and to demonstrate the use of the new Benders’ framework for stochastic capacitated facility location. Last, not least, the report presents updates and additions to the other components and extensions of the SCIP Optimization Suite: the LP solver SoPlex, the modeling language Zimpl, the parallelization framework UG, the Steiner tree solver SCIP-Jack, and the mixed-integer semidefinite programming solver SCIP-SDP. T3 - ZIB-Report - 18-26 KW - constraint integer programming KW - linear programming KW - mixed-integer linear programming KW - mixed-integer nonlinear programming KW - optimization solver KW - branch-and-cut KW - branch-and-price KW - column generation framework KW - parallelization KW - mixed-integer semidefinite programming KW - Steiner tree optimization Y1 - 2018 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:0297-zib-69361 SN - 1438-0064 ER -